fixed-log.c

const uint64_t a1 = 1431655765, a2 = 858993459, a3 = 613566760, a4 = 477218078,
               a5 = 390489239, a6 = 328862160, a7 = 317788895;

// 2 + a1*x^2 + a2*x^4 + a3*x^6 + a4*x^8 + a5*x^10 + ...

const uint64_t ln2 = 1488522236;

int log_test(int x)
{
    if (x <= 0)
        return 0;
    uint64_t y = x, f, s, hfsq;
    int shift = __builtin_clzll(y) - 32;
    y <<= shift;
    f = y - 0x80000000u;
    s = (f << 31) / ((2ull << 31) + f);
    hfsq = (f * f) >> 32;  // (f * f / 2) >> 31
    uint64_t s2 = (s * s) >> 31, s4 = (s2 * s2) >> 31;
    y = (s4 * (a2 + ((s4 * (a4 + ((s4 * a6) >> 31))) >> 31))) >> 31;
    y += (s2 * (a1 + ((s4 * (a3 + ((s4 * (a5 + ((s4 * a7) >> 31))) >> 31))) >> 31))) >> 31;
    y = (y * s) >> 31;
    y = f - (hfsq - ((s * (hfsq + y)) >> 31));
    return ((23 - shift) * ln2 + y) >> 23; // (31 - shift - 8) >> (31 - 8)
}